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Sample path average optimality of Markov control processes with strictly unbounded cost

Oscar Vega-Amaya (1999)

Applicationes Mathematicae

We study the existence of sample path average cost (SPAC-) optimal policies for Markov control processes on Borel spaces with strictly unbounded costs, i.e., costs that grow without bound on the complement of compact subsets. Assuming only that the cost function is lower semicontinuous and that the transition law is weakly continuous, we show the existence of a relaxed policy with 'minimal' expected average cost and that the optimal average cost is the limit of discounted programs. Moreover, we...

Sample-path average cost optimality for semi-Markov control processes on Borel spaces: unbounded costs and mean holding times

Oscar Vega-Amaya, Fernando Luque-Vásquez (2000)

Applicationes Mathematicae

We deal with semi-Markov control processes (SMCPs) on Borel spaces with unbounded cost and mean holding time. Under suitable growth conditions on the cost function and the mean holding time, together with stability properties of the embedded Markov chains, we show the equivalence of several average cost criteria as well as the existence of stationary optimal policies with respect to each of these criteria.

Second Order optimality in Markov decision chains

Karel Sladký (2017)

Kybernetika

The article is devoted to Markov reward chains in discrete-time setting with finite state spaces. Unfortunately, the usual optimization criteria examined in the literature on Markov decision chains, such as a total discounted, total reward up to reaching some specific state (called the first passage models) or mean (average) reward optimality, may be quite insufficient to characterize the problem from the point of a decision maker. To this end it seems that it may be preferable if not necessary...

Semi-Markov control models with average costs

Fernando Luque-Vásquez, Onésimo Hernández-Lerma (1999)

Applicationes Mathematicae

This paper studies semi-Markov control models with Borel state and control spaces, and unbounded cost functions, under the average cost criterion. Conditions are given for (i) the existence of a solution to the average cost optimality equation, and for (ii) the existence of strong optimal control policies. These conditions are illustrated with a semi-Markov replacement model.

Stationary optimal policies in a class of multichain positive dynamic programs with finite state space and risk-sensitive criterion

Rolando Cavazos-Cadena, Raul Montes-de-Oca (2001)

Applicationes Mathematicae

This work concerns Markov decision processes with finite state space and compact action sets. The decision maker is supposed to have a constant-risk sensitivity coefficient, and a control policy is graded via the risk-sensitive expected total-reward criterion associated with nonnegative one-step rewards. Assuming that the optimal value function is finite, under mild continuity and compactness restrictions the following result is established: If the number of ergodic classes when a stationary policy...

Stochastic dynamic programming with random disturbances

Regina Hildenbrandt (2003)

Discussiones Mathematicae Probability and Statistics

Several peculiarities of stochastic dynamic programming problems where random vectors are observed before the decision ismade at each stage are discussed in the first part of this paper. Surrogate problems are given for such problems with distance properties (for instance, transportation problems) in the second part.

Strong average optimality criterion for continuous-time Markov decision processes

Qingda Wei, Xian Chen (2014)

Kybernetika

This paper deals with continuous-time Markov decision processes with the unbounded transition rates under the strong average cost criterion. The state and action spaces are Borel spaces, and the costs are allowed to be unbounded from above and from below. Under mild conditions, we first prove that the finite-horizon optimal value function is a solution to the optimality equation for the case of uncountable state spaces and unbounded transition rates, and that there exists an optimal deterministic...

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